In this episode, Dr. Huxtable says that the children hate putting up Christmas lights. This fact is proven during Season 8's "Clair's Place."
This is the fourth and final episode featuring Peter running out of the house, after the Huxtable's "Haunted House" scares him. After this episode, Peter would flee no more.
When Rudy and her friends make a recording of spooky noises, then play it back while trying to scare Cliff, the noises on the tape go on much longer than when the kids recorded it. Did they use a tape with a recording loop?
Just as Cliff is coming home with the new drill and his Halloween favors, he comes through the back door to greet the kids and show them the "scary" things he bought. He comes in, slams the door, and it sounds like it shuts, but if you look closely, it doesn't shut. It bounces and reopens.
Cliff: I'm so smart, I'm smarter than me.